Abstract: In this paper we consider the problem of computing 2-D Cauchy principal value integrals of the form

where S is either a rectangle or a triangle, and is integrable over S, except at the point where it has a second-order pole. Using polar coordinates, the integral is first reduced to the form

where denotes the finite part of the (divergent) integral. Then ad hoc products of one-dimensional quadrature rules of Gaussian type are constructed, and corresponding convergence results derived. Some numerical tests are also presented.